For the line y=2/5x+9, what will be the angle this line makes with the x-axis?
Answers
Answer:
21.8014 degrees (to 4 decimal places)
Step-by-step explanation:
The equation y=2/5x+9 forms a certain angle with the x-axis. Note that all lines parallel to y=2/5x+9 also form the same angle with the x-axis, due to Corresponding Angles (the fact that the original line has a y-intercept of 9 is irrelevant). Therefore, we could simplify this problem slightly by considering the angle that y=2/5x (a y-intercept of 0) forms with the x-axis.
To find the angle that this line makes with the x-axis, we'll need the vertex (the origin -- let's call this point "B"), and one point on each of two rays from the vertex (Let Ray #1 be the ray from the origin directly to the right; and let Ray #2 be the ray from the origin extending into Quadrant I -- up and to the right, along the equation y=2/5x).
One point on Ray #1 is (5,0) -- it is on the positive x-axis. Call this point "A"
One point on Ray #2 is (5,2) -- inputting "5" for x, the result for y is "2" Call this point "C"
y = 2/5 * (5) = 2To find the angle (Angle ABC), observe that the three points form a right triangle (the angle CAB is a right angle because the two lines are perpendicular).
To solve for [tex]\angle ABC[/tex], recall the definition of the tangent function:
[tex]tan(\theta)=\dfrac{opposite}{adjacent}[/tex]
The Opposite side, side AC, is just the height (or the y-value) of point C. So, opposite = 2.
The Adjacent side, side BA, is just the x-coordinate of point A (and also point C). So adjacent = 5.
Substituting these known values into the tangent function, we get the following:
[tex]tan(m\angle ABC)=\dfrac{2}{5}[/tex]
To solve for the measure of angle ABC, we need to apply the inverse tangent function (also known as arctangent).
[tex]arctan(tan(m\angle ABC)=arctan(\dfrac{2}{5})[/tex]
The left side simplifies because they are inverse functions:[tex]m\angle ABC=arctan(\dfrac{2}{5})[/tex]
Calculating the right side of the equation (rounding to 4 decimal places):
[tex]m\angle ABC \approx 21.8014^{o}[/tex]
Related Questions
Question content area top Part 1 Point B has coordinates (3,2). The x-coordinate of point A is −9. The distance between point A and point B is 15 units. What are the possible coordinates of point A
Answers
The possible coordinates of point A are (-9, -7) and (-9, 11).
What are coordinates?Coordinates refers to a set of numbers that are used to identify the position of a point in a space, usually defined by an x-axis, y-axis, and in sometimes a z-axis.
Let the y-coordinate of point A be y. Then the coordinates of point A are (-9, y).
Using the distance formula, we have:
√[(3 - (-9))² + (2 - y)²] = 15
Simplify the equation:
√[(12)² + (2 - y)² = 15
Square both sides of the equation, we get:
(12)² + (2 - y)² = 15²
144 + (2 - y)² = 225
(2 - y)² = 225 - 144
(2 - y)² = 81
We now take the square root of both sides:
2 - y = ±9
Solve for y in each case, we get:
y = 2 - 9 = -7 or y = 2 + 9 = 11
Therefore, the possible coordinates of point A are (-9, -7) and (-9, 11).
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!!I NEEEDD HELPPP!! Please helppp :(
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The customer would save $492 in the first year by switching to Intellivision.
The customer would save $207 in the second year by switching to Intellivision.
For the third year, it would be cheaper to stick with ElectroniSource.
How to find the savings ?To calculate the savings for the first year, we need to find the total cost for ElectroniSource and compare it to the flat fee from Intellivision for all three services.
The savings for the first year by switching to Intellivision would be:
$1,632 - $1,140 = $492
Therefore, the customer would save $492 in the first year by switching to Intellivision.
After the first year, Intellivision raises the rates by 25%. So the new flat fee for the second year would be:
$95 + ($95 x 25%) = $118.75
The savings for the second year by switching to Intellivision would be:
$1,632 - $1,425 = $207
Therefore, the customer would save $207 in the second year by switching to Intellivision.
For the third year, Intellivision raises the rates by 16% compared to the second year. So the new flat fee for the third year would be:
$118.75 + ($118.75 x 16%) = $137.78
Therefore, for the third year, it would be cheaper to stick with ElectroniSource, which costs $1,632 for the year, compared to Intellivision, which costs $1,653.36 for the year.
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Solve the following system of equations using Gauss-Jordan elimination method. (Hint: your given Ax=b, you should solve for the inverse of A and obtain x= A A. 4x1 + 3x2 + x3 = 2
B. x1 + x2 + x3 = 3 C. 2x1 + 5x2 + 2x3 = 1
Answers
The Gauss-Jordan elimination method is used to obtain the inverse of a matrix and solve a system of equations. The solution for the given system is x1 = 2/3, x2 = 5/3, x3 = 2/3.
We can represent the given system of equations in the matrix form as
| 4 3 1 | | x1 | | 2 |
| 1 1 1 | * | x2 | = | 3 |
| 2 5 2 | | x3 | | 1 |
Let's perform Gauss-Jordan elimination to obtain the inverse of the matrix A.
Augment the matrix with an identity matrix of the same order:
| 4 3 1 | | 1 0 0 | | ? ? ? |
| 1 1 1 | * | 0 1 0 | = | ? ? ? |
| 2 5 2 | | 0 0 1 | | ? ? ? |
Use row operations to transform the left side of the augmented matrix into an identity matrix:
| 4 3 1 | | 1 0 0 | | ? ? ? | | 1 0 0 |
| 1 1 1 | * | 0 1 0 | = | ? ? ? | =>| 0 1 0 |
| 2 5 2 | | 0 0 1 | | ? ? ? | | 0 0 1 |
To achieve this, we can subtract 2 times the second row from the third row, and subtract 4 times the second row from the first row:
| 4 3 1 | | 1 0 0 | | ? ? ? | | 1 0 0 |
| 1 1 1 | * | 0 1 0 | = | ? ? ? | =>| 0 1 0 |
| 0 3 0 | | 0 -2 1 | | ? ? ? | | 0 0 1 |
Next, we can divide the second row by 3 to obtain a leading 1 in the second row, and subtract 3 times the second row from the first row:
| 1 0 -1 | | 1 -1 1/3 | | ? ? ? | | 1 0 0 |
| 0 1 0 | * | 0 1 0 | = | ? ? ? | =>| 0 1 0 |
| 0 0 1 | | 0 -2 1 | | ? ? ? | | 0 0 1 |
Finally, we can add the third row to the first row and subtract the third row from the second row
| 1 0 0 | | 1 -1 4/3 | | ? ? ? | | 1 0 0 |
| 0 1 0 | * | 0 1 2 | = | ? ? ? | =>| 0 1 0 |
| 0 0 1 | | 0 -2 1 | | ? ? ? | =>| 0 0 1 |
Hence, we have obtained the inverse of the matrix A as
| 1 -1 4/3 |
| 0 1 2 |
| 0 -2 1 |
We can now find the solution vector x by multiplying the inverse of A with the vector b
| x1 | | 1 -1 4/3 | | 2 |
| x2 | = | 0 1 2 | * | 3 |
| x3 | | 0 -2 1 | | 1 |
Performing the matrix multiplication, we get
| x1 | | 2/3 |
| x2 | = | 5/3 |
| x3 | | 2/3 |
Therefore, the solution of the given system of equations is
x1 = 2/3
x2 = 5/3
x3 = 2/3
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Solve the quadratic function by factoring x^2 +10x+9-0
Answers
The solution for the quadratic function by factoring x^2 +10x+9-0 is x = -1 and x = -9.
Given that the equation is x^2 +10x+9-0.
To solve the quadratic equation x^2 + 10x + 9 = 0 by factoring, follow the steps given below:
First we need to find two numbers that multiply to 9 and add to 10. These numbers are 1 and 9:
x^2 + 10x + 9 = (x + 1)(x + 9)
So the solutions to the equation are the values of x that make each factor equal to zero:
x + 1 = 0 or x + 9 = 0
Solving for x in each case, we get:
x = -1 or x = -9
Therefore, the solutions to the quadratic equation x^2 + 10x + 9 = 0 are x = -1 and x = -9.
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how do i change a mixed number to a improper fraction and simplify
Answers
Answer:
To change a mixed number to an improper fraction quickly we can multiply the whole number by the denominator, add the numerator and then write that over the original denominator.
trapezoid ABCD is similar to trapezoid EFGH what is the value of M
Answers
The value of M is 4.
The value of M represents the length of the segment that connects the midpoints of the non-parallel sides of trapezoid ABCD. To find the value of M, we can use the fact that the trapezoids are similar.
Now, let's label the points where MN intersects sides BC and FG as P and Q, respectively. We can use the fact that MN is parallel to sides BC and FG to show that triangles BMP and FQN are similar to trapezoids ABCD and EFGH, respectively.
Therefore, we can write:
BM/AB = MP/CD = k
and
FQ/EF = QN/GH = k
Since we know that AB/EF = k, we can substitute this into the first equation to get:
BM/EF = MP/GH
Similarly, we can substitute FQ/EF = k into the second equation to get:
FQ/EF = QN/GH
Now, let's combine these two equations to get:
(BM + FQ)/EF = (MP + QN)/GH
But we know that BM + FQ = EF, and MP + QN = GH. Therefore, we can simplify the equation to get:
EF/EF = GH/GH
Or simply:
1 = 1
This means that our calculations are correct, and that we can use the ratio k to find the value of M. Specifically, since MN is parallel to AB and CD, we know that the length of MN is equal to half the difference between the lengths of AB and CD. Therefore, we can write:
M = (1/2)(AB - CD)/k
When we apply the values on it, then we get,
M = (1/2) (56 - 48) / 1
M = (1/2) x 8 = 4
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Eric and victoria are working on a project. eric has completed 3/8 of the project and and victoria has completed 1/3 of the project.
"(help me with this pls asap)"
Answers
Eric has completed 37.5% (or 0.375) of the project, while Victoria has completed 33.3% (or 0.333) of the project. Together, they have completed approximately 70.8% (or 0.708) of the project.
If Eric and Victoria are working on a project and Eric has completed 3/8 of the project, and Victoria has completed 1/3 of the project, then to find the total portion of the project completed, you can add their individual contributions: (3/8) + (1/3).
To add these fractions, you need a common denominator, which is 24 in this case. So, you can rewrite the fractions as (9/24) + (8/24). Adding them together gives you a total of 17/24 of the project completed by both Eric and Victoria, which is equal to 70.8% (or 0.708).
*complete question: Eric and victoria are working on a project. eric has completed 3/8 of the project and and victoria has completed 1/3 of the project. Calculate the total work they have completed together.
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Can Someone Help me with this It is not easy
[ 40 POINTS]Ф
Answers
Answer:
4^9262144Step-by-step explanation:
You get 4 pennies for a first job, 16 pennies for the second job, 64 pennies for the 3rd job, and you want to know how many pennies you get for the 9th job, if each job quadruples the pay.
Exponential expressionWe can write the number of pennies as a power of 4:
job 1: 4^1 penniesjob 2: 4^2 penniesjob 3: 4^3 pennies...job 9: 4^9 penniesYou will get 4^9 pennies for the 9th job.
That is 262144 pennies.
<95141404393>
Jayden just accepted a job at a new company where he will make an annual
salary of $41000. Jayden was told that for each year he stays with the
company, he will be given a salary raise of $2500. How much would Jayden make as a salary after 4 years working for the company? What would be his salary after t years?
Answers
Jayden's starting salary is $41000 per year. If he stays with the company for one year, he will receive a raise of $2500, bringing his new salary to $43500. If he stays for two years, he will receive another raise of $2500, bringing his salary to $46000.
If he stays for three years, he will receive a third raise of $2500, bringing his salary to $48500. And finally, if he stays for four years, he will receive a fourth raise of $2500, bringing his salary to $51000.
Therefore, after four years working for the company, Jayden's salary would be $51000 per year.
After t years, Jayden's salary would be calculated as follows:
- After one year: $41000 + $2500 = $43500
- After two years: $41000 + ($2500 x 2) = $46000
- After three years: $41000 + ($2500 x 3) = $48500
- After four years: $41000 + ($2500 x 4) = $51000
- After t years: $41000 + ($2500 x t).
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A random sample of 318 students from a large college were asked if they are planning to visit family during Thanksgiving break. Based on this random sample, a 95% confidence interval for the proportion of all students at this college who plan to visit family during Thanksgiving break is 0. 78 to 0. 98. Which of the following is the correct interpretation of the confidence interval?
Group of answer choices
1)We are 95% confident that the interval from 0. 78 to 0. 98 captures the true proportion of all students at this college who plan to visit family during Thanksgiving break.
2)We are 95% confident that the interval from 0. 78 to 0. 98 captures the true mean of all students at this college who plan to visit family during Thanksgiving break.
3)95% of students at this college are going home during Thanksgiving Break.
4)None of these are correct
Answers
The correct interpretation of the given confidence interval is 95% confidence that the true proportion of all students at this college who plan to visit family during Thanksgiving break is between 0.83 and 0.93 .
Then the required answer to the given question is Option D.
Let us consider a random sample of 318 students from a large college that were asked if they are planning to visit family during Thanksgiving break. Now placing the given random sample, the proportion of 95% confidence interval of all students at this college that planned to visit family during Thanksgiving break is 0.78 to 0.98 .
The formula for evaluating the confidence interval is
CI = p ± z × √((p × (1 - p)) / n)
Here,
CI = confidence interval,
p = sample proportion,
z = z-score corresponding to the desired level of confidence (in this case, 95%)
n is the sample size .
Applying the values
CI = 0.88 ± 1.96 × √((0.88 × (1 - 0.88)) / 318)
CI = 0.88 ± 0.05
CI = (0.83, 0.93)
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Given n with chord AB, which point lies on the perpendicular bisector of AB?
Answers
The Midpoint of AB ((x1 + x2)/2, (y1 + y2)/2) lies on the perpendicular bisector of AB.
Which point lies on the perpendicular bisector of AB?Assuming that chord AB is a straight line segment, the point that lies on the perpendicular bisector of AB is the midpoint of AB. This is because the perpendicular bisector of a line segment is a line that passes through the midpoint of the segment and is perpendicular to it.
Therefore, to find the point that lies on the perpendicular bisector of chord AB, we need to find the midpoint of AB. This can be done by finding the average of the x-coordinates and the average of the y-coordinates of points A and B, respectively.
Let (x1, y1) and (x2, y2) be the coordinates of points A and B, respectively. Then the midpoint of AB is:
((x1 + x2)/2, (y1 + y2)/2)
This point lies on the perpendicular bisector of AB.
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What is the volume of the regular pyramid to the nearest whole number?
Regular pyramid
1452 cm
594 cm
1188 cm
1029 cm
Answers
The volume of the regular pyramid is 1188 cm³.
What is a regular pyramid?A regular pyramid is a pyramid whose base is a regular polygon and whose lateral edges are all equal in length.
To calculate the volume of the regular pyramid, we use the formula below
Formula:
V = bhH/6....................... Equation 1Where:
V = Volume of the pyramidb = Base of of the triangleh = Height of the triangleH = Height of the pyramidFrom the question,
Given:
H = 22 cmb = 18 cmh = 18 cmSubstitute these values into equation 1
V = 18×18×22/6V = 1188 cm³Hence, the right option is C. 1188 cm³
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Lines AC and BD intersect at point O. Lines AC and BD intersect at point O. If m∠AOD = (10x − 7)° and m∠BOC = (7x + 11)°, what is m∠BOC?
A. 6°
B. 53°
C. 89°
D. 106°
Answers
Answer: the answer is B. 53°
Step-by-step explanation:
(10x-7) = (7x+11)
10x-7-7x =7x+11-7x
3x-7=11
3x-7+7=11+7
3x=18
x=6
Plug 6 into angle ∠BOC
7x+11
7(6)+11
42+11
53°
Given that lines AC and BD intersect at point O, we know that ∠AOD and ∠BOC form a linear pair. It means that the sum of those angles should be 180° since the straight line's sum is 180°.
Therefore, we can create the equation (10x - 7)° + (7x + 11)° = 180°, where x is the variable we need to find.
By combining like terms, we simplify this equation to 17x + 4 = 180.
To isolate x, we have to subtract 4 from both sides of the equation, resulting in 17x = 176.
Now, dividing both sides by 17, we find that x equals approximately 10.35.
Finally, to find measure of ∠BOC, we just need to substitute the value of x we found into the expression of m∠BOC: m∠BOC = 7*10.35 + 11, which is approximately 83.47°.
Based on the choices given, C. 89° is the closest to our calculated value. Therefore, the answer is C. 89°.
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A doctor saw 8 patients a day for 7 days. How many patiencents did he see altogether
Answers
The doctor saw 56 patients altogether during the 7 days.
To find out how many patients the doctor saw altogether, we need to use multiplication.
Identify the number of patients seen per day (8 patients).
Identify the number of days the doctor worked (7 days).
Multiply the number of patients per day by the number of days worked.
8 patients/day × 7 days = 56 patients.
The doctor saw 8 patients per day for 7 days, so the total number of patients he saw in a week is
Therefore, the doctor saw a total of 56 patients in 1 week.
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Greg uses a triangular area of his backyard as a garden. If the area of his backyard is 1,248 square feet, what is the area of the garden?
Answers
Unfortunately, we don't have enough information to determine the area of the garden. We would need to know the dimensions of the backyard and/or the garden to calculate their areas.
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The music industry has steadily moved from selling music in a physical format such as records, eight tracks, cassettes, and CDs telling music in digital formats. In 2001, the music industry sold $26.5
billion of music in the physical format. Each year after 2001, the amount of sales of music constantly decreased by 10%.
Select the function P(t), where P represents the sales, in billions of dollars, of music in the physical format and t represents the number of years since 2001.
P(0) 26 5/0 1
Answers
Answer:
P(t)=26.5 (0.1)^t
Step-by-step explanation:
A dealer paid $10,000 for a boat at an auction. At the dealership, a salesperson sold the boat for 30% more than the auction price. The salesperson received a commission of 25% of the difference between the auction price and the dealership price. What was the salesperson’s commission?
Answers
The commission of the salesperson is $750 if he received a commission of 25% of the difference between the auction price and the dealership price.
The salesperson's commission can be calculated by first finding the dealership price, which is 30% more than the auction price of $10,000.
30% of $10,000 = $3,000
Dealership price = $10,000 + $3,000 = $13,000
Next, we need to find the difference between the dealership price and the auction price
$13,000 - $10,000 = $3,000
The salesperson's commission is 25% of this difference
25% of $3,000 = $750
Therefore, the salesperson's commission is $750.
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(c) Katrina recorded the average rainfall amount, in inches, for two cities over the course of 6 months. City A: {5, 2. 5, 6, 2008. 5, 5, 3} City B: {7, 6, 5. 5, 6. 5, 5, 6} (a) What is the mean monthly rainfall amount for each city? (b) What is the mean absolute deviation (MAD) for each city? Round to the nearest tenth. (c) What is the median for each city?
Answers
The mean monthly rainfall amount for City A is approximately 338.3 inches, and for City B, it is 6 inches.
The mean absolute deviation for City A is approximately 92.8 inches, and for City B, it is 0.5 inches.
The median for City A is 5.5 inches, and for City B, it is 6 inches.
(a) To find the mean monthly rainfall amount for each city, we sum up the rainfall amounts for each city and divide by the number of months.
For City A:
Mean = (5 + 2.5 + 6 + 2008.5 + 5 + 3) / 6 = 2030 / 6 ≈ 338.3 inches per month
For City B:
Mean = (7 + 6 + 5.5 + 6.5 + 5 + 6) / 6 = 36 / 6 = 6 inches per month
So, the mean monthly rainfall amount for City A is approximately 338.3 inches, and for City B, it is 6 inches.
(b) The mean absolute deviation (MAD) is a measure of the average distance between each data point and the mean. To calculate the MAD, we first find the absolute difference between each data point and the mean, sum them up, and then divide by the number of data points.
For City A:
Absolute differences from the mean: |5 - 338.3|, |2.5 - 338.3|, |6 - 338.3|, |2008.5 - 338.3|, |5 - 338.3|, |3 - 338.3|
MAD = (333.3 + 335.8 + 332.3 + 1670.2 + 333.3 + 335.3) / 6 ≈ 557.0 / 6 ≈ 92.8
For City B:
Absolute differences from the mean: |7 - 6|, |6 - 6|, |5.5 - 6|, |6.5 - 6|, |5 - 6|, |6 - 6|
MAD = (1 + 0 + 0.5 + 0.5 + 1 + 0) / 6 ≈ 3 / 6 = 0.5
So, the mean absolute deviation for City A is approximately 92.8 inches, and for City B, it is 0.5 inches.
(c) To find the median, we arrange the rainfall amounts in ascending order and find the middle value. If there are an even number of data points, we take the average of the two middle values.
For City A: {2.5, 3, 5, 5, 6, 2008.5}
Median = (5 + 6) / 2 = 11 / 2 = 5.5 inches
For City B: {5, 5.5, 6, 6, 6.5, 7}
Median = 6 inches
So, the median for City A is 5.5 inches, and for City B, it is 6 inches.
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A father and his three children decide on all matters with a vote. Each member of the family gets as many votes as their age. Right now, the family members are 36, 13, 6, and 4 years old, so the father always wins. How many years will it take for the three children to win a vote if they all agree? Show your work.
Answers
Answer:
Step-by-step explanation:
Answer:
13 years
Step-by-step explanation:
Intuition for how sons can collectively win after a certain period of time:- After a certain period of time the father's age will increase by that certain period of time (say 5 years) but for the sons (since there are 3 of them) their collective age will increase by three times that of their father (5 for each 1 one them). Therefore there exist a time after which collective increase in sons' age can cover the current gap of 13 years.
the the radian measure of each angle 1. 45 2.225 3. pie over 2
4. 3pie over 4
5. 3 radians
Answers
The radian measure of each angle:
1. π/4
2. 5π/4
The degree measure of each angle:
3. 90°
4. 135°
5. 540°
How to find the radian measure of each angle?To find the radian measure of each angle, use π/180 to multiply each angle and then simply. That is:
1.) 45 * π/180 = π/4 radian
2.) 225 * π/180 = 5π/4 radian
To find the degree measure of each angle, use 180/π to multiply the angles and then simply. That is:
3.) π/2 * 180/π = 90°
4.) 3π/4 * 180/π = 135°
5.) 3π * 180/π = 540°
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The function f(x) = 1. 25x2 models the packaging costs, in cents, for a box shaped like a rectangular prism. The side lengths are 2x in. , 2x in. , and 0. 5x in. What are reasonable domain and range values for this function, if the longest side length of the box can be no greater than 20 in. ? Write the answers in interval notation
Answers
The range of the function f(x) is Range: [0, 125] In interval notation, this can be written as [0, 125] if the longest side length of the box can be no greater than 20 in.
The function f(x) = 1.25x^2 models the packaging costs, in cents, for a rectangular prism-shaped box with side lengths of 2x in., 2x in., and 0.5x in.
We need to determine the reasonable domain and range values for this function, given that the longest side length of the box can be no greater than 20 in.
Since the longest side length is 20 in., we know that:
2x ≤ 20
x ≤ 10
Therefore, the domain of the function f(x) is all real numbers less than or equal to 10, or: Domain: [-∞, 10]
To find the range of the function, we need to examine the behavior of the function as x varies. Since the coefficient of x^2 is positive, the function is quadratic with a minimum value at x = 0. Therefore, we know that the range of the function must start at its minimum value, which is f(0) = 0, and increase as x increases.
To determine the upper limit of the range, we can evaluate f(x) when x = 10 (the maximum value of x allowed):
f(10) = 1.25(10)^2 = 125
Therefore, the range of the function f(x) is:
Range: [0, 125]
In interval notation, this can be written as [0, 125].
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Dolly went to the Walmart and he buy 14 teddy bears and 3 dolls for 158 $ and her sister went to the Gwinnett place mall and she buy 8 teddy bears and 12 dolls for 296 $. If they both buy same brand bears and dolls, then what is price of one teddy bear and one doll? (use matrices multiplication to solve system of equations. ) (Show work)
Answers
According to formed equations, the price of one teddy bear and one doll is $7 and $20 respectively.
Let us represent the teddy bear as x and dolls as y. Now, framing the equation for Dolly and Gwinnett.
Cost of teddy bear × number + cost of dolls × number = total expenditure
14x + 3y = 158 : equation 1
8x + 12y = 296 : equation 2
Divide the equation by 4
2x + 3y = 74 : equation 3
Subtraction equation 3 from equation 1
14x + 3y = 158
- 2x + 3y = 74
12x = 84
x = 84/12
x = $7
So, the cost of teddy bear = $7
keep the value of x in equation 3 to find the cost of y
2×7 + 3y = 74
14 + 3y = 74
3y = 74 - 14
3y = 60
y = 60/3
y = $20
Thus, the cost of teddy bear and dolls are $7 and $20.
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how many different triangles can be formed by side lengths 2 cm, 7cm, and 70 degrees angle formed by these given sides?
Answers
8: Hector’s Math test grades for the final
quarter are 89, 93, 100, 98, and 95. He has one
more test to take this quarter. All tests count
equally. What is the minimum grade Hector must
make on the last test in order to obtain an
average of at least 93?
Answers
Hector needs to score at least a 97 on his last test to obtain an average of at least 93 for the final quarter.
The average grade for the final quarter can be calculated by summing up all the grades and dividing by the total number of tests. In this case, Hector has taken 5 tests, and his grades are 89, 93, 100, 98, and 95. Therefore, his current total score is 89+93+100+98+95 = 475.
To obtain an average of at least 93, Hector's total score for all 6 tests should be at least 93*6 = 558.
So, Hector needs to score a minimum of 558 - 475 = 83 on his last test. Since all tests count equally, Hector needs to score at least 83% on his last test. Therefore, the minimum grade Hector must make on the last test in order to obtain an average of at least 93 is 97 (rounded up from 96.6).
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Please help!!! prove triangle abe is congruent to triangle cde
Answers
To prove that triangle ABE is congruent to triangle CDE, we need to show that all three corresponding pairs of sides and angles are equal.
Firstly, we can see that angle ABE is congruent to angle CDE as they are both right angles (90 degrees).
Secondly, we can see that side AB is congruent to side CD as they are both the hypotenuse of their respective triangles.
Lastly, we need to show that side AE is congruent to side CE. We can do this by using the Pythagorean theorem.
In triangle ABE, we have:
AE^2 = AB^2 - BE^2
In triangle CDE, we have:
CE^2 = CD^2 - DE^2
Since AB is congruent to CD and BE is congruent to DE (they are corresponding sides), we can substitute and simplify:
AE^2 = CD^2 - DE^2 - BE^2
CE^2 = CD^2 - DE^2
Therefore, if we subtract the second equation from the first, we get:
AE^2 - CE^2 = -BE^2
Since BE is a positive length, -BE^2 is negative. Therefore, AE cannot be equal to CE.
Thus, we have shown that triangle ABE is not congruent to triangle CDE.
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Marcella drew a scale drawing of her plan to plant 6 rows of 8 trees in her orchard. The orchard is 70 meters long and 50 meters wide. Marcella used a 7-inch-wide rectangular grid for the drawing. What is the scale Marcella used for her drawing?
Answers
The scale Marcella used for her drawing is 7 inches : 50 meters
Calculating the scale used for her drawingThe statements in the question are given as
Dimension of the orchard is 70 meters long and 50 meters wide. Width of the scale drawing = 7 inches rectangular gridThe above statements imply that we have the following scale ratio
Scale = Scale measurement : Actual measurement
When the given values are substituted in the above equation, the equation becomes
Scale = 7 inches : 50 meters
The above cannot be simplified because 7 and 50 do not have common factors
So, it means that the scale Marcella used for her drawing is 7 inches : 50 meters
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3. Find a quadratic polynomial whose one zero is 5 + √3 and sum of the zeroes is 10.
Answers
Answer:
f(x) = x² - 10x + 22
Step-by-step explanation:
Let's assume the quadratic polynomial as:
f(x) = ax² + bx + c
Now we know that if one of the zeroes is 5 + √3, then the other zero must be 5 - √3 (because complex roots always come in conjugate pairs).
So the sum of the zeroes will be:
(5 + √3) + (5 - √3) = 10
10 = 2 * 5
The product of the zeroes will be:
(5 + √3) * (5 - √3) = 25 - 3 = 22
Now, using the sum and product of zeroes, we can write:
b/a = 10
c/a = 22
Solving for b and c, we get:
b = -10a
c = 22a
Substituting these values in f(x), we get:
f(x) = a(x - 5 - √3)(x - 5 + √3)
Expanding the right-hand side:
f(x) = a[(x - 5)² - (√3)²]
f(x) = a(x² - 10x + 22)
Comparing the coefficients of f(x) with ax² + bx + c, we get:
a = 1, b = -10, c = 22
Therefore, the quadratic polynomial is:
f(x) = x² - 10x + 22
A chef is going to use a mixture of two brands of Italian dressing. The first brand contains 5% vinegar, and the second brand contains 8% vinegar. The chef wants to make 300 milliliters of a dressing that is 7% vinegar. How much of each brand should she use?
First Brand: ?
Second Brand: ?
Answers
The chef should use 100 milliliters of the first brand and 200 milliliters of the second brand.
To create a 300 milliliters dressing with 7% vinegar using two brands of Italian dressing, we can use a system of equations to find the quantities of each brand needed.
Let x be the amount of the first brand (5% vinegar) and y be the amount of the second brand (8% vinegar).
First equation (total volume):
x + y = 300
Second equation (vinegar percentage):
0.05x + 0.08y = 0.07 * 300
Now, solve the system of equations:
From the first equation, y = 300 - x
Substitute this into the second equation:
0.05x + 0.08(300 - x) = 21
Expand and simplify:
0.05x + 24 - 0.08x = 21
0.03x = -3
Now, divide by 0.03:
x = 100
Now, find the value of y:
y = 300 - x = 300 - 100 = 200
So, the chef should use 100 milliliters of the first brand and 200 milliliters of the second brand.
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Arturo has $480 to spend at a bicycle store for some new gear and biking outfits.
Assume all prices listed include tax.
• He buys a new bicycle for $201. 87.
• He buys 3 bicycle reflectors for $9. 82 each and a pair of bike gloves for $15. 79.
• He plans to spend some or all of the money he has left to buy new biking outfits
for $32. 80 each.
Write and solve an inequality which can be used to determine o, the number of outfits
Arturo can purchase while staying within his budget.
Inequality: 1
Submit Answer
attempt 1 out of 2
Answers
Answer:
Step-by-step explanation:
201.87 + 3(9.82) + 15.79 + 32.80(o) < 480
247.12 + 32.80(o) < 480
32.80(o) < 480 - 247.12
32.80(o) < 232.88
o < 232.88/32.8
o < 7.1
He can purchase 7 outfits and stay within the $480 budget
Which angle in AXYZ has the largest measure? 4 Y A. LX B. LY C.
Answers
(A) ∠X is the largest angle in the given triangle as the side opposite is also the largest.
What are angles?An angle is formed when two straight lines or rays meet at a single terminal.
The place where two points converge is known as an angle's vertex. The name "angle" comes from the Latin word "angulus," which means "corner."
Two lines that meet at the same point or two planes that meet at the same line form a geometric figure.
The angle in degrees separates these lines or planes.
So, we know that:
The side opposite to the largest angle is also the largest side of the triangle and vica-versa.
Remembering this we can easily conclude that ∠X is the largest angle as the largest is 9 units and X is opposite of the side YZ which measures 9 units.
Therefore, (A) ∠X is the largest angle in the given triangle as the side opposite is also the largest.
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Correct question:
Which angle in AXYZ has the largest measure?
A. ∠X
B. ∠Y
C. ∠Z
D. Cannot be determined
